1. Project Management
Projects are unique, one-time operations designed to accomplish a specific set of objectives in a limited timeframe
Project managers are responsible for managing the cost and timely completion of the project
PERT/CPM are tools to support project managers

2. Schware Foundry Inc.
Schware Foundry, Inc., a metalworks plant, has been given 16 weeks by the local environmental protection agency to install a complex air-filter system on its main smokestack.
The project manager has identified the 8 key activities that are necessary to complete the smokestack modification as well as the estimated completion times for each activity. (These activities are shown on the next slide)

3. H Inspection & Testing F,G 2 weeks
Immediate Expected
Activity Description Predecessors Time
A Build internal components weeks
B Modify roof and floor weeks
C Construct collection stack A weeks
D Pour concrete & install
frame B weeks
E Build high temp. burner C weeks
F Install control system C weeks
G Install air pollution device D,E weeks
H Inspection & Testing F,G weeks

4. Project Management
Determine all specific activities associated with the project along with estimates for the amount of time required to complete each activity. Identify the interdependencies of the activities
Create a network to depict the sequential relationships between the activities
Perform PERT or CPM to determine the critical activities and expected project completion time.

5. Critical Path Analysis Definitions
A path is a sequence of activities that leads from the starting node of the project to the finishing node of the project
The length of the path is the sum of the activity times of the activities comprising the path
The critical path is the path with the longest length of time. It represents the minimum project completion time.

6. Critical Activity Definitions
Critical activities are the activities which make up the critical path. Any delays with these activities will hurt the project completion time.
Slack time is the delay an activity can experience without hurting the project completion time, assuming that the other activities stay on track with their schedule.

7. Information Recorded for Each Node
ESTi
EFTi i ti
LSTi
LFTi
ti = time required to perform activity i
ESTi = earliest possible start time for activity i
EFTi = earliest possible finish time for activity i
LSTi = latest possible start time for activity i
LFTi = latest possible finish time for activity i

8. CPM Analysis Algorithm
Step 1: Make a forward pass through the network as follows: For each of these activities, beginning at node i, compute:
Earliest Start Time = the maximum of earliest finish times for all of its immediate predecessors
Earliest Finish Time = (Earliest Start Time) + (Time to complete activity i).
The project completion time is the maximum of the Earliest Finish Times at the completion node.

9. CPM Analysis Algorithm
Step 2: Make a backwards pass through the network as follows: Move sequentially backwards from the last node, N, to node N-1, to node N-2, etc. At a given node, j, compute:
Latest Finish Time = the minimum of the latest start times for all activities that immediately follow the activity (For node N, this is the project completion time.)
Latest Start Time = (Latest Finish Time) - (Time to complete activity j).

10. CPM Analysis Algorithm
Step 3: Calculate the slack time for each activity by:
Slack = (Latest Start) - (Earliest Start) or
= (Latest Finish) - (Earliest Finish).
A critical path is a path of activities, from node 1 to N, with 0 slack times.
Note that the slack for each noncritical activity is shared with other noncritical activities on the same path.

11. PERT
In the three-time estimate approach, the time to complete an activity is assumed to follow a Beta distribution.
An activity’s mean completion time is:
t = (a + 4m + b)/6
An activity’s completion time variance is:
((b-a)/6)2
a = the optimistic completion time estimate
b = the pessimistic completion time estimate
m = the most likely completion time estimate

12. Immediate Optimistic Most Likely Pessimistic
Activity Time Time Time
A week weeks 3 weeks
B week s weeks 4 weeks
C week weeks 4 weeks
D weeks weeks 5 weeks
E weeks weeks 6 weeks
F weeks weeks 4 weeks
G weeks weeks 7 weeks
H week weeks 3 weeks

13. PERT
In the three-time estimate approach, the critical path is determined as if the mean times for the activities were fixed times.
The overall project completion time is assumed to have a normal distribution with mean equal to the sum of the means along the critical path and variance equal to the sum of the variances along the critical path.

14. Example: ABC Associates
Consider the following project:
Immed. Optimistic Most Likely Pessimistic
Activity Predec. Time (Hr.) Time (Hr.) Time (Hr.)
A —
B —
C A
D A
E A
F B,C
G B,C
H E,F
I E,F
J D,H
K G,I

15. Example: ABC Associates
Activity Expected Time Variance
A /9
B /9 C
D /9
E /36
F /9
G /9
H /9 I
J /9
K /9

16. Example: ABC Associates
Activity ES EF LS LF Slack
A *critical B
C * D E
F * G H
I * J
K *
The estimated project completion time is the Max EF at node 7 = 23. Critical Path (A-C-F-I-K)

17. Example: ABC Associates
Probability the project will be completed within 24 hrs
2 = 2A + 2C + 2F + 2H + 2K
= 4/ / /9
= 2
 =
z = ( )/(24-23)/1.414 = .71
From the Standard Normal Distribution table:
P(z < .71) = =